Balloon and method of manufacturing the same



July 31, 1962 w. F. HUCH ETAL BALLOON AND METHOD OF MANUFACTURING THE. SAME Filed April 30, 1959 4 Sheets-Sheet 1 INVENTORS WILLIAM F. HucH Eowmzu P NEY JOHN R. WINCKLER ,w'afl/m ATTYS' July 31, 1962 w. F. HUCH ET AL I 3,047,252

BALLOON AND METHOD OF MANUFACTURING THE SAME 7 Filed April 30, 1959 4 Sheets-Sheet 2 INVENTORS WILLIAM F HWIH EDWARD P. NEY JOHN R. WINCKLER MATTYS.

July 31, 1962 w. F. HUCH ETAL BALLOON AND METHOD OF MANUFACTURING THE SAME 4 Sheets-Sheet 3 Filed April 30, 1959 INVENTORS WILLIAM F.HucH EDWARD R NEY JOHN R. WINCKLER ,ZMMV ATTYS y 31, 1962 w. F. HUCH ETAL 3,047,252

BALLOON AND METHOD OF MANUFACTURING THE-SAME Filed April 50, 1959 4 Sheets-Sheet 4 INVENTORS WILUAM F.HucH EDWARD P. NEY

JOHN R.WINCI LER fl ATTYS.

United States Patent 3,047,252 BALLOON AND METHOD OF MANUFACTURING THE SAME William F. Huch, St. Paul, and Edward P. Ney and John R. Winckler, Minneapolis, Minn, assignors, by mesne assignments, to the United States of America as represented by the Secretary of the Navy Filed Apr. 30, 1959, Ser. No. 810,201 20 Claims. (Cl. 244-31) This invention relates to high altitude balloons, including those used to carry' equipment for investigating unknowns of the mesosphere, and is concerned more particularly with improved balloons and methods of making the same.

This invention embraces improvements over the subject matter of the US. patent application of Rudolph B. Thorness, Serial No. 667,728, filed June 24, 1957, for Balloon and Method of Making the Same, issued November 22, 1960, as Patent No. 2,961,194.

An object of this invention is to simplify, expedite, and reduce the cost of high altitude balloons and their manufaeture.

Another object is to provide a method of making a single-gore balloon of any desired volume from a roll of film.

A further object is to provide a method of making a film balloon in a substantially continuous sealing operation.

It is also an object to provide an improved method of making a balloon having four mutually equidistant apices.

An additional object is to provide an improved method of making a pillow balloon.

Another object is to provide a method of fabricating, from sheeting of commercially available width, a singlegore balloon of any desired volume without waste of any sheet material.

A further object is to provide a balloon constructed of spiraled rectangular film.

An additional object is to provide a single-gore balloon of any desired size.

A further object is to provide a sealed gored balloon requiring no inspection of seals for leakage after the balloon has been fabricated.

Another object is to provide a balloon manufacturing method requiring small Working space regardless of the size of the balloon.

Further objects and advantages of the invention will appear as the description proceeds.

The invention will be better understood on reference to the following description and the accompanying more or less schematic drawings, in which:

FIG. 1 shows a rectangular sheet from which a model regular tetrahedron can be made in accordance with the invention.

FIGS. 2 to 4 show the sheet in three successive stages in the making of the model.

FIG. 5 shows the completed model.

FIG. 6 is a fragmentary view of an apparatus which can be employed in making high altitude balloons in accordance with the invention, and the film as the manufacture of a balloon is about to start.

FIG. 7 is similar to FIG. 6 but shows the partially made balloon as the spiral sealing progresses.

FIG. 8 is a fragmentary view showing an early stage in the balloon fabrication process, with the first apex completed.

FIG. 9 shows the second apex completed.

FIG. 10 shows how a regular tetrahedral type balloon might appear at ceiling altitude, the seams being omitted.

FIG. 11 is a bottom plan view of an inflated balloon 3,047,252 Patented July 31, 1962 "ice of the regular tetrahedral type, made in accordance with the invention and having relatively few spiral turns and showing the curved appearance of the spiral seam.

FIG. 12 shows a rectangular sheet from which a model square pillow can be made in accordance with the invention.

FIGS. 13 and 14 correspond to FIGS. 4 and 5 but relate to the square pillow.

The aforesaid Thorness application discloses a balloon having four apices which, when the balloon is fully inflated (i.e., when the lift gas in the bottom of the balloon is at the same pressure as the ambient atmospheric air), are mutually equidistant, the balloon being made in a form capable of assuming the shape of a regular tetrahedron from a film tube having an axial length equal to times its fiat width, and fabricated out of a plurality of rectangular panels or gores extending longitudinally parallel to the tube axis and sealed at their longitudinal margins, the tube being then sealed at each end in a line normal to and bisected by the tube axis, the lines being oriented to each other, the ends of each line defining two of the four apices. This requires that a number of identical gores be cut to the same rectangular size, handled, and placed in proper juxtaposition for longitudinal marginal sealing, and a like number of longitudinal sealing operations performed to produce a tube, using a table at least as long as the gore length and hence requiring a large working space, and the two tube-end-sealing operations must also be performed. 'For a multi-gore balloon having, when fully inflated, a volume on the order of about one million cubic feet, for example, the table in accordance with present practice would be at least about 200 feet long. The tube-end seals of course cross the longitudinal seals, and special care must be taken at each of the numerous crossings to guard against leakage thereat.

Balloons and their manufacture in accordance with the instant invention are free of the foregoing and other disadvantages, as will appear.

Ina regular tetrahedron, the line joining any two apices is oriented 90 from and is of the same length as and does not intersect the line joining the other two apices, and these lines have a common perpendicular bisector.

A rectangular sheet, properly dimensioned, lends itself to being generated spirally into a regular tetrahedron in accordance with this invention. To insure that the line joining any two apices will be oriented 90 to the line joining the other two apices, the number of spiral halfturns must be a predetermined one of a family of numbers consisting of /2, 1 /2, 2 /2, N /2. The length of the sheet must be the product of the spiral half-turn length and the number of spirial half-turns.

Referring now more particularly to the drawings, there is shown at 20 (FIG. 1) a rectangular sheet from which a model regular tetrahedron may :be spirally generated in accordance with the invention by the steps outlined below:

The sheet 20 is folded at A (FIG. 2) and the left edge portion AC placed so as to confront the left edge portion AB, and these edge portions are taped in that relation, forming a first corner at A. The end edge CD is then folded at its midpoint E to arrange the parts as shown in FIG. 2, the distances BI and DJ then being co-equal. Now the portion ED] is shifted so as to confront the end edge portion EC with the end edge portion ED (FIG. 3) and these portions are then taped together, forming a second corner at E, the right margin F thus becoming at D a continuation of the left margin G, The remainder BJH of the left edge is then placed in confronting relation to the right edge portion DIM, as in FIG. 4, and there taped. At this stage the partially completed article is in the form of a pocket whose open end is irregular and defined by an edge PRUM and an edge PQM. This open end is then spread, to enable the end edge PQH to be so folded at its midpoint Q as to confront the end edge portion QH with the end edge portion QP, and these two portions are taped together, forming a third corner at Q, and leaving an endless edge PRUM, where P and M are now together. The edge portion MUT is one-half the length of the endless edge PRUM, so that the edge portion PRT is the complemental half; these halfleng'th portions are then placed together and taped, providing from M a continuation of the seam which started at A, the continuation terminating, and forming the fourth corner, at T, the article now being fully closed and having four apieces A, E, Q, and T, a spiral seam ABMT, and two identical relatively short seams EB and QM. If now the article is creased along AE, EQ, QA, AT, ET, and QT, and each crease remains straight, the apieces A, E, Q, and T will be mutually equidistant, so that the article .will have the shape of a regular tetrahedron (FIG. The tape is omitted from the drawing for clarity.

The distance AC, which is denoted by a and called the starting distance, since it is at the start of the spiral sealing operation, is determined by the equation a=0.577Kw where K is the number of spiral half turns and w is the effective or net width of the rectangular sheet, i.e., the distance between the centerlines of two successive convolutions of the spiral seam; and the length s of the rectangle is determined by the equation $w=aK+ 0.43310 These equations are derived as follows:

The area X of a regular tetrahedron in terms of the distance L between any two apieces is From FIG. 4 it is evident that the distance c=a+BJ is the length of a half-turn of the spiral. Since the three right triangles AEJ, ABE, and EBI are similar, it is apparent that The area of the regular tetrahedron in terms of w, c, and K is obviously It is accordingly evident from (1), (3), and (4) that so that The area of the rectangle in terms of its length sand width w is obviously X =sw Substituting for X as in (3),

so that it follows that s= aK-l- Or, substituting for a as in (5),

In the model regular tetrahedron shown in FIG. 5, K is 2 /2. If, in that model, w is 2", then a is 2.89" and s is 8.09".

From (2) it is evident that from which it is obvious that (ca) 0 as K- oo From FIG. 4 it is apparent that azL: :Lzc and thus L== /ac so that ac- L as (c-a) 0 w in will be negligible in Equation 4, so that it is sufiiciently accurate to consider a as equal to L. This fact has been alluded to above and is demonstrated as follows.

The volume V of a regular tetrahedron in terms of L is Hence L =8.48V From (4) and (7),

and thus ingptw Obviously, then, in the last equation the value 5.06 is negligible, so that a may be considered as equal to L in (7), and thus it is proper to write for the regular tetrahedron. Solving,

pp y If K had turned out to be other than a whole number plus /2for example 78. 6-a value of 78.5 or 79.5,

preferably the closer of the two, would have had to be used for K, and a would have had to be recomputed, to

obtain a regular tetrahedron close to the desired volume.

Applying (6), the length of film used is The additional 1.95, which for practical purposes can be taken as 2, though seemingly negligible, must nevertheless be taken into account. The reason for this is that since a quarter-turn (90) is 102' long, a distance of 2' subtends an angle of nearly 2. It follows, then, that failure to take into account the final 2' will result in an irregular tetrahedron in which one line of apices will be oriented about 88", instead of 90, to the other line of apices. This 2 discrepancy is to be avoided where a maximum volume-to-weight ratio is desired, which is obtained when the figure is capable of assuming the shape of a regular tetrahedron.

An apparatus suitable for use in making a balloon out of polyethylene film in accordance with the invention is shown more or less schematically at 30 in FIGS. 6 and 7, and comprises a machine 32 having among other things means at the back 34 of the machine for journaling a roll 36 of film 38; a journaled cross bar 40 which for convenience will be referred to as a reference bar; a guide 42 on which the left margin G of the film is slidably supported as it comes ofi the roll and after it has passed over the bar; a suitable heat sealer, such as a hot air jet sealer 44 over and spaced from the guide and which in operation directs a jet of hot air down toward the guide; one or more additional cross bars (not shown) which support the full width of the film as it advances to the front 46 of the machine; and a pair of endless belts 48 forward of the guide and adapted to grip and advance the film. The machine 32 may be driven by any suitable means, such as a series-wound DC motor (not shown) controlled by a foot-operated rheostat (not shown) which permits smooth starting and variable speed control by the machine operator. The jet sealer 44 is in sealing position when the machine is running; when the machine is not running, the sealer is normally out of sealing position but may be moved into and out of sealing position.

An odometer roller 50 is adapted to rest on the film 38 on the right end portion 52 of the reference bar 40 and to be turned by the film as the film advances. The apparatus 30 also comprises a hand-rotatable round basket 54 formed of nylon cloth or other suitable material which will not snag the film.

Using such an apparatus, a 1,000,000- cubic foot regular tetrahedron can be formed of polyethylene film using a starting distance a of 204', a 1 lap, an effective width of 4 /2, and 78 /2 spiral half-turns, as follows:

(1) The free end 56 (FIG. 6) of the film 38 is handpulled off the film roll 36 and passed over the reference bar 40 and under the odometer roller 50. When the end 56 is just under the odometer roller 50, the odometer reading is preferably zero. Then the film 38 is pulled further, the left margin G being passed over the guide 42 and under the nozzle of the sealer 44 (which is then inoperative) and between the belts 48, whereupon the machine operator, stationed at the back 34 of the machine 32, starts the machine to feed the film. The film 38 issuing from the forward part 46 of the machine 32 is guided into the basket 54 by an operator thereat, and he turns the basket as the film continues to advance, so that the film in the basket will not be snarled. When the odometer 50 reads 204', the machine 32 is stopped, the left part of the film, where it rests on the reference bar 40, is marked with the station numeral 0, and the right part of the film is marked with the station numeral 2 (FIGS. 7 and 8).

(2) The left margin G of the film 38 ahead of the station 0 is then folded at that station to lap 1" over the left margin back of that station (FIG. 8); the film from the roll 36 is pulled forward by hand until the fold rests on the guide 42 in position to be sealed; the sealer 44 is used to seal the lapped portions at the fold, forming the first apex (FIG. 8), at which a prominent mark is made for a purpose which Will appear in connection with step 5, below; and the film is pulled further and the lapped portions back of and adjacent the fold are sealed. When the told is between the belts 48, the machine 32 is again started, with the sealer 44 continuing in operation, and the part of the left margin which is in the basket 54 near the left rear of the machine is raised by the machine operator and allowed to slip between his fingers (FIG. 7) while he guides it to maintain the lap uniform. The sealing is continued until the film end 56 from the basket 54 is about a few feet short of the reference bar 40, where upon the machine is stopped and by virtue thereof the sealer 44 rendered inoperative. The seam is indicated at 58.

(3) Now the film end 56 is center-folded and the resulting halves fin sealed together, as at 60 (FIG. 9), by hand, forming the second apex E at the fold, the right margin F of the film thus becoming a continuation of the left margin G of the film at what were formerly the terminal portions of the film end.

(4) Operation of the machine and sealing are now resumed, the free end portion of the fin becoming sealed as shown, or spread-eagled (not shown), to the left margin G therebelow. When station 2, after emerging from the basket 54, reaches the reference bar 40, the machine is stopped and the film over the right portion 52 of the bar is marked with the station numeral 4.

(5) The machine operation is again alternately resumed and stopped, and at successive stops the film at the right over the bar 40 is marked with the station numerals 6, 8, 10 until station 50 is marked, whereupon the odometer reading is noted. When the balloon is completed, it is to be packed in a sack in an arrangement which will facilitate launching, and for that purpose the apex which is to be at the bottom of the balloon is inserted first, and the top of the balloon is positioned at the upper end of the sack so that the top can be pulled out first, inasmuch as the top portion is to form the infiation bubble and hence is the first part of the balloon dealt with in the launching procedure. The apex A is selected to be the bottom of the balloon, and of course the center or top of what is to be the crown of the balloon will then lie at the center of the equilateral triangle (of the regular tetrahedron) opposite that apex. The top will therefore be located /=,K half-turns (i.e., 601K +0.433w) feet), from the film end 56. K in this instance being 78.5 and w being 4.5, the distance, in feet, of the balloon top from the leading end 56, measured lengthwise of the film, is (52%)(204)+1.3. Since the station 50 on the film is in fact 51 x 204 feet from the film end 56, due to the fact that station is 204 from the end, the top will be located (1 /3)(204)+1.3=273.3 feet back of station 50. Hence, having noted the odometer reading when station 50 is marked, the operator will know where to place the mark indicating the balloon top insofar as its distance back of station 50 is concerned. The place is marked prominently so that it may be readily picked out when the fabricated balloon is bunched in the basket 54. A selected spot (near the top), where the inflation tube is to be attached, is also marked prominently.

(6) The machine operation is again alternately resumed and stopped, and the film at the right over the bar 40 is successively marked with the numerals 52, 54 the last station mark applied being 76. The balloon is to have 78.5 half-turns, but, as is apparent from the discussion under step 5, station 76 is in fact 77 x 204 feet from what was originally the film end 56. As the total length footage of film is to be it follows that the film is to be cut from the roll at a distance of feet behind station 76.

(7) Accordingly, when the mark 76 is made, the operator notes the odometer reading, then the operation is resumed and again stopped when the odometer records the 308 additional feet, whereupon the film is cut along the reference bar 40.

(8) The trailing film end thus cut from the roll 36 is center-folded and the resulting halves fin-sealed by hand as in the manner noted in step 3, forming the third apex as at Q (FIGS. 4 and and making an endless margin of the unsealed remainder of the right margin F.

(9) The operation is resumed, the two halves of the endless margin formed in step 8 being guided into sealing position by the machine operator, until the halves are sealed together up to a point about a few feet or so from where the seal would normally be completed.

(10) The material is then removed to the left from the machine and the remainder of the halves of the endless margin of step 9 are fed by hand and sealed, forming the fourth apex as at T (FIGS. 4 and 5) and thus completing the regular tetrahedron.

A machine sealing rate of about 20 feet per minute has been found suitable.

For a high altitude inelastic film balloon of given volume V of the regular tetrahedron, effective width w, lap, and unit weight y per square foot of film, the values of a, K and the total weight, Z, of the film can be readily computed from the equations:

After the balloon has been fabricated, a hole or slit is made in the balloon at the inflation tube mark, for an inflation tube (not shown), of polyethylene or other suitable film, to be attached thereat as by heat sealing or adhesive taping, and to hang outside of the balloon. Then the balloon is strung out in gathered untwisted form by hand, starting at the apex A and ending at the top, and at the same time all of the air trapped in the balloon during fabrication is progressively squeezed out of it. The inflation tube is then attached and temporarily closed; then the balloon is coiled, accordion-folded, or otherwise arranged in the sack, with the balloon top uppermost and so that the balloon will not snarl as it is removed at the launching site.

If the balloon is to serve as a superpressured balloon, it will of course be closed when launched. If it is to have an appendix, provision for escape of lift gas at the bottom or other part of the balloon may be made in any manner, such provision forming no part of this invention.

The same apparatus may be employed using a single film twice as wide as the roll 36. Rolls on which the film is folded double, with the two longitudinal edges arranged at one end of the roll and the center fold at the other end of the roll, are commercially available. With such a roll arranged so that the two edges are at the left side of the machine, the left margin of the upper layer will correspond to the right margin of the film 38, and will be guided to the right away from the sealer and belts until after it has been brought around in the basket to where the machine operator is stationed, and he will guide it into lapped position over the part of the left margin of the lower layer which has not yet reached the sealer, preparatory to scaling in the manner described above in step 2. With such film the station numbers are conveniently marked on the left margin of the upper layer over the reference bar just before the upper layer is guided out of the way of the sealer.

If the balloon is to be made of Mylar film the inability of Mylar film to fuse together is gotten around by the use of a special tape. For the machine sealing, a roll of such tape may be carried by the machine in a position to have the tape fed over the lower left margin so that the tape will be sandwiched between that margin and the other margin emerging from the basket, the upper and lower surfaces of the tape being adhesive to Mylar when heated. A separate piece of such tape is used in each hand-sealing operation. Suitable for cementing together the Mylar film portions is a l-mil Mylar core G. T. Schjeldahl /8" wide tape coated on each face with l-mil of T-lO resin. The weight of the tape used will of course enter into the computation of the total weight of the balloon. The sealer 44 or other suitable heat sealing means may be employed.

Other methods of forming the seams may be resorted to within the frame of the invention.

The spiral seam can be inspected by the attendant at the front of the machine and imperfections, if any, corrected by him by a hand sealer while the machine is running, so that such effort would not increase the fabrication time. However, it has been found that there is no need for inspection, the machine sealing being reliable. Balloons can be made in accordance with this invention with approximately the same number of manhours required for merely inspection and correction of seals of balloons made by former methods.

An embodiment of the apparatus briefly described above and which has been employed in the manufacture of balloons of up to several million cubic feet fully inflated volume is located in a room 20' x 20' and comprises a machine which is about 4 high, 5 wide, and 6 long and a basket which is 14' in diameter and about 3' deep at its center.

Instead of resorting to station marking as noted above, the machine operator could merely wait until the odometer reading equals /as to mark the balloon top and then until the reading equals s to cut off the material from the roll. However, this procedure is cumbersome and moreover could lead to error, where, as is found to be the case occasionally, the material in spots may be wrinkled as it passes under the odometer roller, giving an inaccurate odometer reading. The track-keeping method noted above, in accordance with which the number of a-lengths is marked in stations on the film, is both more convenient and more accurate.

In a square pillow balloon having the same area of material as a regular tetrahedral balloon, it is apparent from the foregoing and FIG. 14 that where X represents the area, L represents the width of the square pillow balloon, and L represents the distance between any two 'apices of the regular tetrahedron. Hence L,,= 4 L=.93L 9 The volume of a fully inflated square pillow balloon has been found empirically to be about 7% less than that of a fully inflated regular tetrahedron type balloon of the same film area. Hence, applying (7) and (9) the volume V, of a fully infiated square pillow balloon can be expressed as so that L VEEI 1.75%;

From FIG. 14, it is evident that wherefore Inasmuch as in a square or other rectangular pillow DJzg: zgza it is apparent that it is clear that in a square pillow from which obviously a =0.5K,,w (11) 1 0 and The length of a spiral half-turn 0,, is obviously 2 c D a p M D so that the length s of the film is to K w w s =K (a (ZDKD+ an Since, from (12) it follows that, for a square pillow s =a K +0.5w (13 A model pillow may be spirally generated from a reotangular sheet in the manner in which a tetrahedron is formed, the difference residing in the fact that, for the pillow, the number of spiral halt-turns K is necessarily 1 or a larger integer, to insure that all four apices will fall in the same plane, regardless whether the pillow is to be square or of non-square rectangular form. FIG. 14 shows a square pillow byway of example, made in accordance with the invention from the sheet 70 (FIG. 12). To make a flat pillow from a given width of rectangular sheet, one need merely decide upon the dimensions L x i select on a longitudinal margin, for example the left margin, a point A whose distance is L from the midpoint E of an end edge, for example the upper end edge, of the material, compute the number K,, of the spiral half-turns needed to provide the other desired dimension i of the pillow, and proceed in the manner indicated in FIGS. 2 to 4, the stage in FIG. 13 corresponding to that in FIG. 4. For the general case of the pillow,

In FIGS. 12 to 14, as in FIGS. 2 to 5, the tape is omitted for clarity.

In FIGS. 12 to 14, K is 3, and the square pillow shown in FIG. 14 is completely closed and has its four apices respectively at A, E, R, and Q, a spiral seam AIB'JIUIMIR! and two relatively short seams EB and Q'M.

In FIGS. 12 to 14 the reference characters correspond generally to those in FIGS. 1 to 5, one exception being that in FIGS. 12 to 14 the letter T does not appear.

It will be noted that for the general case, i.e., regardless whether the four-apex balloon is capable of assuming the shape of a tetrahedron or of a pillow in accordance with the invention,

and, since E ca+ (2) it follows that Kw saK+- For any spirally generated tetrahedral type balloon in accordance with the invention, K is other than an integer; for such a balloon in which the line defined by two apices is to the line defined by the other two apices, K is one-half of an odd integer; for such a balloon in which the apices are mutually equidistant, that is, where the tetrahedron is regular, K is equal to and is one-half of an odd integer. For any spirally generated pillow type balloon in accordance with the invention, K is an integer greater than zero; for a square pillow, K is equal to and is an integer greater than zero.

In the manufacture of a high altitude pillow balloon in accordance with the invention, the apparatus noted above may be used. The method differs from that described above in that the step of locating the top is omitted, inasmuch as one of the apices will be at the top, and conveniently the first and third apices, as formed, and a selected spot (near the top) where the inflation tube is to be attached, could be prominently marked for easy identification in the basket, and the computations and marginal markings made in accordance with the applicable formulae.

Although any suitable film material and thickness may be employed, materials in common use are transparent polyethylene and Mylar, in thicknesses of from about A mil to about 2 mils. Although susceptible to some stretching when subjected to high pressures, the stretching is relatively slight so that these materials are nominally inelastic and inexpansible.

If it be desired to manufacture a balloon in accordance with the invention using film which is substantially wider than commercially available width, this could readily be done. For example, if the width desired were to be three times the effective width w, three rolls 36 could be so arranged that the left margins of the films off the center and right rolls respectively overlap the right margins of the films off the left and center rolls, and heat sealers applied to seal the respective laps to provide the desired composite gore passing into the machine before reaching the basket. For two spirally generated regular tetrahedron type ballocus of the same volume, or two spirally generated square pillow balloons of the same volume, one balloon using a Wider gore than the other of the same type, the starting distance a will be the same in both cases of the type involved (subject to slight modification as noted above if K as computed is other than a member of the family identified with that type), and, in accordance with (5) or (12), as the case may be, K will be smaller for the wider gore balloon than for the narrower gore balloon, and thus the length of the spiral seam and hence the spiral sealing time will be correspondingly reduced.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described.

We claim:

1. A balloon formed of a flexible rectangular sheet, the ends of one margin of the sheet being joined respectively to the corresponding ends of the opposite margin of the sheet, whereby said margins together constitute a first endless rim whose length is substantially twice the length of the sheet and the other two opposite margins constitute respectively second and third endless rims, the first rim having a transverse fold spaced from the second and third rims, a first seam extending in a spiral and commencing at the fold and connecting together the entire first rim portions extending from the fold, each of the second and third rims having a transverse center fold, a second seam commencing at the center fold of the second rim and connecting together the second rim portions extending from the second rim center fold, and a third seam commencing at the center fold of the third rim and connect ing together the third rim portions extending from the third rim center fold.

2. The structure of claim 1, characterized in that where s and w are respectively the length and elfective width of the sheet, a is the distance from said fold of the first rim to the second seam and said distance is at least as short as the distance from said fold of the first rim to the third seam, and

is one-half of any odd integer.

3. The structure of claim 1, characterized in that said fold of the first rim is unequally distant from the second and third seams.

4. The structure of claim 1, characterized in that where s and w are respectively the length and efiective width of the sheet, a is the distance from said fold of the first rim to the second seam and said distance is at least as short as the distance from said fold of the first rim to the third seam, and

is one-half of any even integer greater than zero.

5. The structure of claim 1, characterized in that Fang where s and w are respectively the length and efiective Width of the sheet, a is the distance from said fold of the first rim to the second rim, and

is one-half of an odd integer.

7. The structure of claim 1, characterized in that the first seam is a spiral, and

where s and w are respectively the length and effective width of the sheet, a is the distance from said fold of the first rim to the second seam and said distance is at least as short as the distance from said fold of the first rim to the third seam, and K is the number of half-turns of the spiral and is an integer.

8. The structure of claim 1, characterized in that where s and w are respectively the length and effective width of the sheet, a is the distance from said fold of the first rim to the second seam and said distance is at least as short as the distance from said fold of the first rim to the third seam, and

is an integer greater than zero.

13 9. The structure of claim 1, characterized in that the first two opposite margins are the longer margins of the sheet.

10. The structure of claim 1, characterized in that, measured along the first seam, said fold of the first rim is closer to the second seam than to the third seam, and

where s and w are respectively the length and effective width of the sheet, a is the distance, measured along the first seam, from said fold of the first rim to the second where s and w are respectively the length and effective width of the sheet, a is the distance, measured along the first seam, from said fold of the first rim to the second Seam,

is an integer greater than zero, and

w sinis approximately zero.

12. The structure of claim 1, characterized in that where s and w are respectively the length and effective width of the sheet, a is the distance, measured along the first seam, from said fold of the first rim to one of the second and third seams, and K is the total number of halfturns of the spiral seam and is one-half of one of a group of integers consisting of 13. The structure of claim 1, characterized in that s=Ka Where K is the total number of half-turns of the spiral seam and is one-half of one of a group of integers consisting of are e w w s and w are respectively the length and effective width of the sheet, a is the distance, measured along the first seam, from said fold of the first rim to one of the second and third seams, and

K to

is approximately zero.

14. A method of making a single-gore balloon, comprising the steps of transversely center-folding each end margin of a rectangular film, 'with the same face of the film at the interiors of both folds; longitudinally seaming together the resulting halves of each end margin, whereby an apex is formed at each fold point, and also where,- by the longitudinal margins of the rectangular film become an endless rim; transversely folding the endless rim at a point spaced from the end margins; and longitudinally seaming together the entire rim portions commencing at the latter fold point.

15. A method of making a four-apex balloon, comprising the steps of longitudinally marginally seaming a plurality of rectangular panels of uniform length to form a composite rectangular gore having the same length as an individual panel and a width equal approximately to the sum of the widths of the panels; transversely center-folding each end margin of the composite gore, with the same face of the gore at the interiors of both folds; longitudinally seaming together the resulting halves of each end margin, whereby an apex is formed at each fold point, and also whereby the two longitudinal margins of the composite gore become an endless rim; and longitudinally seaming together the entire lengths of the rim portions extending from a point spaced from the end margins whereby to form an apex at each end of the last-mentioned seam.

16. A method of making a single gore ballon capable of assuming the shape of a regular tetrahedron of volume V from -a rectangular length of film on a roll, comprising the steps of feeding film off the roll; transversely center-folding the exposed end edge of the film, with a predetermined face of the film at the inside of the fold; sealing together the entire resulting half-portions of said end edge, whereby an apex is formed at the fold, and also whereby the longitudinal edges of the film become a single longitudinal margin; transversely folding said margin, with said face at the inside of the latter fold, at a point whose distance a from said end edge is given by the equation commencing, at said point, the spiral sealing together of portions of said margin extending from said point and temporarily stopping when the number of sealed spiral half-turns is about and does not exceed K-l, where K is that one of a family of numbers, consisting of /2, 1 /2, 2 /2 N /2, which is determined from the equation where w is the effective width of the film; cutting the film from the roll at a point whose distance s from the first-mentioned end edge is given by the equation transversely center-folding and longitudinally scaling together the entire resulting halves of the cut .end edge, with said face of the film at the inside of the latter fold, thereby rendering end-less the unsealed portion of said margin; and resuming the spiral sealing unitil half of said endless portion is sealed to the other half thereof.

17. A method of making a single gore ballon capable of assuming the shape of a regular tetrahedron of volume V from a length of transparent limp film on a roll, comprising the steps of feeding film off the roll; transversely center-folding the exposed end edge of the film, with a predetermined face of the film at the inside of the fold; longitudinally sealing together the entire resulting halves of said edge, whereby the longitudinal edges of the film become a single longitudinal margin; transversely folding said margin, with said face at the inside of the latter fold, at a point whose distance a from the end edge is given by the equation commencing the sealing together of the marginal portions from said point and temporarily stopping when the number of sealed spiral half-turns is %K, where and is the total number of half-turns to be made and is one of a family of numbers consisting of A2, 1%, 2 /2 N /z, and w is the effective width of the film; prominently marking the film at the temporary stopping point of the spiral seal; resuming the spiral sealing; cutting off the film from the roll at a distance s from said end edge given by the equation transversely center-folding the cut end edge, with said face at the inside of the latter fold, and sealing together the resulting halves of the cut end edge, thereby rendering endless the unsealed portion of said margin; resuming the spiral sealing until half of said endless portion is sealed to the other half thereof; and, as the spirial sealing progresses substantially from its inception, guiding and confiining the sealed part of the balloon over an area whose greatest dimension is a minor fraction of the distance a.

18. A method of making a single gore square pillow balloon, comprising the steps of feeding film off a roll; transversely center-folding the exposed end edge of the film and sealing together the entire resulting halves of said end edge, whereby the longitudinal margins of the film become a single longitudinal rim; transversely folding the rim at a point which is a predetermined distance a from the end edge; commencing the sealing together of the rim portions from the latter point and temporarily stopping when the number of sealed spiral half-turns is about and does not exceed K-il, where K is a whole number nearest that given by the equation where w is the film width; prominently marking the film at the temporary terminus of the spiral seal and also at the end of the next-to-last of the sealed spiral half-turns to be made; cutting otf the film from the roll at the lastmentioned end, center-folding and sealing together the resulting halves of the cut end edge, thereby rendering endless the unsealed portion of the rim; resuming the spiral sealing until one half of the endless portion is sealed to the other half thereof; and, as the spiral sealing progresses substantially from its inception, guiding and confining the sealed part of the balloon over an area whose greatest dimension is a minor fraction of the distance a.

19. A method of making a single-gore four-apex balloon, comprising the steps of transversely folding a longitudinal margin of a rectangular film panel at a point unequally distant from the end margins of the panel; lapsealing together the longitudinal marginal portions from the fold to a first position somewhat short of the nearer end margin; transversely folding said nearer end margin midway of its length; sealing together the entire lengths of the resulting halves of said nearer end margin, whereby said longitudinal margin forms with the other longitudinal margin a single longitudinal rim whose length is substantially twice the length of the panel; continuing the lap-sealing to a second position somewhat short of the other end margin of the panel; transversely folding said other end margin midway of its length; sealing together the entire lengths of the resulting halves of said other end margin, thereby rendering endless the unsealed portion of the rim; continuing the lap-sealing to a third position somewhat short of the position at which the rim sealing must terminate, and, from said third position, sealing one half of the remainder of the endless portion to the other half thereof.

20. In a method of making a single-gore four-apex balloon, the steps of sealing together the ends of one end margin of a rectangular fih'n panel; sealing together the ends of the other end margin, with the same face of the panel at the inside, whereby the longitudinal margins of the panel become an endless longitudinal rim substantially twice the length of the panel; transversely folding the rim at a point spaced from the end margins, with said face at the inside of the fold, and sealing together one half of the rim to the other half thereof from the fold.

References Cited in the file of this patent UNITED STATES PATENTS 969,732 Tebyrica Sept. 6, 1910 2,666,600 Huch et al. Jan. 19, 1954 FOREIGN PATENTS 187,035 Austria Oct. 10, 1956 

